Local Bifurcation for Steady Periodic Capillary Water Waves with Constant Vorticity

被引：16

作者：

Martin, Calin Iulian ^{[1
]}

机构：

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2013年 / 15卷 / 01期

关键词：

FINITE DEPTH; TRAJECTORIES; UNIQUENESS; AMPLITUDE; SYMMETRY;

D O I：

10.1007/s00021-012-0096-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study periodic capillary waves at the free surface of water in a flow with constant vorticity over a flat bed. Using bifurcation theory the local existence of waves of small amplitude is proved even in the presence of stagnation points in the flow. We also derive the dispersion relation.

引用

页码：155 / 170

页数：16

共 22 条

[1] Symmetry of steady periodic surface water waves with vorticity
Constantin, A
Escher, J
[J]. JOURNAL OF FLUID MECHANICS, 2004, 498 : 171 - 181
[2] Exact steady periodic water waves with vorticity
Constantin, A
Strauss, W
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (04) : 481 - 527
[3] Constantin A., 2011, CBMS NSF REGIONAL C
[4] Symmetry of steady periodic gravity water waves with vorticity
Constantin, Adrian
Ehrnstrom, Mats
Wahlen, Erik
[J]. DUKE MATHEMATICAL JOURNAL, 2007, 140 (03) : 591 - 603
[5] The trajectories of particles in Stokes waves
Constantin, Adrian
[J]. INVENTIONES MATHEMATICAE, 2006, 166 (03) : 523 - 535
[6] Analyticity of periodic traveling free surface water waves with vorticity
Constantin, Adrian
Escher, Joachim
[J]. ANNALS OF MATHEMATICS, 2011, 173 (01) : 559 - 568
[7] Steady Periodic Water Waves with Constant Vorticity: Regularity and Local Bifurcation
Constantin, Adrian
Varvaruca, Eugen
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 199 (01) : 33 - 67
[8] Crandall M.G., 1971, J. Funct. Anal., V8, P321, DOI DOI 10.1016/0022-1236(71)90015-2
[9] AN EXACT SOLUTION FOR PROGRESSIVE CAPILLARY WAVES OF ARBITRARY AMPLITUDE
CRAPPER, GD
[J]. JOURNAL OF FLUID MECHANICS, 1957, 2 (06) : 532 - 540
[10] STEEP, STEADY SURFACE-WAVES ON WATER OF FINITE DEPTH WITH CONSTANT VORTICITY
DASILVA, AFT
PEREGRINE, DH
[J]. JOURNAL OF FLUID MECHANICS, 1988, 195 : 281 - 302

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